Thank you for your question.
I am Dr. Su S. and I will try my best to help you.
Constant discharge can be due to blockage of the tear or lacrimal duct.
It is common in infant.
You have to massage the inner corner of the eye to remove the blockage.
As Chlorsig is not working you need to have repeat evaluation.
Sometimes it can persist for a long time.
Pus can be tested to know the organism and start proper treatment.
If there is block, then it may need intervention by ophthalmologist.
As it already 4 weeks, you should show it to his doctor to have a management plan.
I hope this information will be helpful.
If you have any query, please feel free to ask.
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Wish his healthy life.